Use a fabric cover first to give the plants a chance to get a hold. If it is very steep even strong plants will be washed away before the roots can get a good hold.

Creeping ground cover is the right idea because then you don't have to plant too many plants. A good example of something cheap and very strong is ivy.

You can also plant grass if the area you live in has a natural selection of grasses. Often a wild looking embankment of natural grass looks great, and you only have to cut it once a year after it dries and the seeds fall (so they can grow next year).